Spaceman Fred’s trusty pellet sprayer is held at rest a distance h away from the center of Planet Orb, which has radius R \ll h. The pellet sprayer ejects pellets radially outward, uniformly in the plane of the page. These pellets are all launched with the same speed v, so that a pellet launched directly away from Orb by the pellet sprayer can just barely escape it. What fraction of the pellets eventually lands on Orb? (Hint: you may use the small angle approximation, \sin \theta \approx \theta for \theta \ll 1, where \theta is in radians.)
Left: the pellet sprayer relative to Orb
Right: a close-up of the pellet sprayer
Answer Choices
A. \frac{1}{2 \pi} \frac{R}{h}
B. \frac{1}{\pi} \frac{R}{h}
C. \frac{2}{\pi} \frac{R}{h}
D. \frac{1}{2 \pi} \sqrt{\frac{R}{h}}
E. \frac{1}{\pi} \sqrt{\frac{R}{h}} \leftarrow CORRECT